2,t31. Find the li y-In | 4y+TI. Find the linearization of h at (z,y) = (0,0). 2. Leth(z 3. Let H(z,y)-z' + ya_ 4zy + 2 on the domain DH = { (zw) e R2 l o 2). Find all local and 4,0 y absolut...
2. Let f(x,)-21 be subjoct to the constraint z+y'4. (a) Find all candidate points for the locations of the absolute extrema lying inside the region given by+y4 Co,l) y -l Using the method of Lagrange multipliers, find all candidate points for absolute extreme along the boundary of the region given by+y4. (b) (c) Using your answers above, what are the absolute maximum and absolute minimum values of f over the given region? Clearly label and circle the absolute extrema (give...
Implicit Function Theorem in Two Variables: Let g: R2 → R be a smooth function. Set {(z, y) E R2 | g(z, y) = 0} S Suppose g(a, b)-0 so that (a, b) E S and dg(a, b)メO. Then there exists an open neighborhood of (a, b) say V such that SnV is the image of a smooth parameterized curve. (1) Verify the implicit function theorem using the two examples above. 2) Since dg(a,b) 0, argue that it suffices to...
pleease solve them for me now pleeeaaase
some of them have multiple answers
x²-v If L= lim (x, y) + (0,0) X x+v then along y = mx, so limit exist L 1-mo 1+ m2 along path x = my, and limit does not exist L = m2 -1 0 m +1 along the path X = my and limit does not exist L m-1 0 m + 1 along y=mx? and limit does not exist L 1.-mo 1 +...